Take off speeds can be derived from Airbus performance charts, but the process can be rather tedious when numerous factors (meteorological, airfield conditions, aircraft technical issues, CG on the 320) are involved.
Most operators use a third party performance software like FOVE or LPCNG which is an approved alternative and much more user friendly. The Flight Management system calculates the V approach and V lowest selected airspeeds for landing, but does not calculate the takeoff speeds. The take off flap setting also needs to be calculated, along with a method of reducing engine thrust, known as Flexible temperature. This limits the take off thrust by allowing the engine computer to act as if the ambient temperature is much higher than it actually is, which reduces engine wear while still allowing normal safety and performance margins.
The incident you speak of is a prime example of a series of small errors and oversights that nearly lead to catastrophe.
While entering the flight's take off data into the performance program, the first officer made a simple error on one of the digits of the gross takeoff weight. This resulted in performance for an aircraft weighing 200 tons instead of 300 tons, a considerable difference. Most airlines SOP's call for both pilots to make separate performance calculations and then cross check to avoid these errors. In this case it was not done, despite there being two crews on the flight deck.
During the preflight preparation there were several other opportunities to cross check this data and see the inaccuracy of the result. One value the FMS calculates is the best lift over drag speed, known to Airbus pilots as "green dot speed" for how it is displayed on the speed tape. The heavier an aircraft is, the higher this speed will be aerodynamically. When running performance on the computer, the Green Dot speed computed by the software was around 225 knots, which any 340 pilot all tell you is extremely slow for a heavy fuel laden 300 ton aircraft. The FMS calculated a Green Dot above 252 knots. This should have been a warning bell to an experienced crew, especially since this number was recorded. It is thought because the numbers are easily transposed (2-2-5 and 2-5-2) that this could have also been overlooked.
The lower than normal V1, VR, and V2 speeds should also be a warning, however the crew had just flown a shorter leg from New Zealand with a much lower weight, so the speeds are not out of the realm of possibility.
Another gate should have been the abnormally long acceleration time, as a 340 training captain pointed out to me, the average time from stop to V1/Vr is around 45-50 seconds at that weight, and well over a minute had gone by on this roll... most pilots start a timer on the takeoff roll, but this can also be subjective.
As in most incidents, it can be seen as a series of errors in a chain of events rather that a major flaw in one part of the equation.